The kinship2 R Package for Pedigree Data: Supplementary Material
Jason P. Sinnwell, Terry M. Therneau and Daniel J. Schaid
Division of Biomedical Statistics and Informatics, Department of Health Sciences Research,
Mayo Clinic, Rochester, MN 55905
This supplementary document provides additional details and examples for the methods
described in the application note entitled ``kinship2: An R package for pedigree data''. The
examples below make use of Figure 1 of the main document, a 17-subject pedigree containing
four generations, identical twins, and a consanguineous marriage.
PEDIGREE PLOTS
As a brief example, let us assume we have a data frame in R named fam1 with columns:
subjid as a unique id; dad and mom for subject id of each subject's parents (0 if a founder, i.e., no
parents in the pedigree); sexcode as 1 or 2 for male or female; and disease and vitalstatus
indicator variables for disease and vital status. Below shows an example of how to construct the
pedigree object and then plot it:
R> ped1 <- with(fam1, pedigree(id=subjid, dadid=dad,
momid=mom,
sex=sexcode, affected=disease,
status=vitalstatus))
R> plot(ped1)
The status argument expects the vital status indicator and the affected argument expects an
indicator of disease status. The affected argument can also be a matrix, which provides a way to
store multiple indicator variables for each subject that can be used in plot symbols or simply used
later in analyses.
Figure S1 shows a detailed pedigree plot created from subjects 1-10 of the full pedigree
shown in Figure 1 of the main document. The plot shapes are split into as many portions as there
are indicator variables in the affected matrix of the pedigree object. This example has three
indicators, only one of which indicates disease status. The pedigree.legend function created the
legend in the top right; indicating which portion of the shape shading indicates a positive status
for the three variables in the affected matrix: disease, smoker, and availstatus. Additionally, the
plot method allows the subject id to be alternate text. Supplementary figure S1 has the subject
identifier concatenated with a character string created from the indicator available in the object's
affected matrix, separated by a line-break character. Finally, though not shown here, the plot
allows subject-specific colors, which applies to the plot symbol and identifier.
PEDIGREE TRIMMING
The pedigree.shrink function iteratively removes subjects given their availability status
(e.g., genetic data available) and an affected status, from a pedigree in the following order,
until the pedigree is of a desired bit size.
1. Uninformative subjects, i.e., unavailable (no genetic data available) with no available descendants
2. Available terminal subjects with unknown affected status if both parents are available
3. Unkown affected status
4. Unaffected
5. Affected
The first two steps are always run to shrink the pedigree, regardless of the desired bit size. If
after these steps the bit size is not met, the algorithm iteratively shrinks the pedigree by
preferentially removing subjects, in the order of steps 3 to 5. If there are multiple subjects that
meet the condition under consideration, one of them is randomly chosen to be removed. The
method’s default bit size of 16 was chosen because some linkage software has memory
requirements that increase exponentially by pedigree size, but a different bit size may be chosen
for determining informative subjects in genome-wide association and sequencing studies where
cost may be more of a limiting factor.
Given the affected information shown in Figure 1, and an availability status that is TRUE for
all affected individuals, the pedigree in Figure 1 shrinks to the pedigree in supplementary Figure
S1 after just the first two steps of pedigree.shrink, with a bit size of (2*6)-4=8. The command to
shrink the pedigree in Figure 1 to the pedigree in Figure S1 is shown below, followed by a call to
the pedigree.shrink print method.
R> shrink1 <- pedigree.shrink(ped1, avail=availstatus)
R> print(shrink1)
Pedigree Size:
Original
Only Informative
Trimmed
N.subj Bits
17
19
10
8
10
8
Unavailable subjects trimmed:
13 15 16 17
Non-informative subjects trimmed:
11 12 14
Trimming a pedigree can also be carried out by the built-in R sub-setting utilities, using the
indices of the subjects that are to be either kept or removed. For example, the pedigree in Figure
S1 can be created from the pedigree in Figure 1 with either of the following commands.
R> pedS1 <- ped1[-c(11,12,13,14,15,16,17)]
R> pedS1 <- ped1[1:10]
KINSHIP MATRIX EXAMPLES
Supplementary Table S1 shows the kinship matrix for the pedigree shown in supplementary
Figure S1. Ignoring for a moment the fourth generation, subject 10, the kinship coefficients for
the first three generations follow a simple pattern, where self kinship coefficients are 0.50,
parent-offspring coefficients are 0.25, and grandparent-grandchild coefficients are 0.125.
Avuncular coefficients for subject pairs 4-7, 3-8, and 3-9 are also 0.125, and cousins, pairs 7-8
and 7-9, are half that at 0.0625. Also, because subjects 8 and 9 are identical twins, the kinship
coefficients with each other are the same as their self kinship coefficient. Subject 10 in the
fourth generation introduces a few scenarios handled seamlessly by the kinship function. First,
subject 10 is equally-related to her uncle as to her father because subjects 8 and 9 are identical
twins. Furthermore, subject 10’s self kinship coefficient is greater than 0.5 because of
inbreeding; that is, there is a 1/32=0.03125 chance that the two alleles at a given locus are
identical by descent from either of her great-grandparents. The inbreeding coefficient for any
subject i can be obtained by hi=2Ki,i-1; therefore, h10=0.0625. The X chromosome kinship
matrix for the same 10-subject pedigree is in Table S2, where we have included the sex
(M=Male, F=Female) for each subject with the identifiers in rows and columns so it is clear to
follow the differences from Table S1.
Table S1 Kinship matrix on autosomes for 10-member pedigree in Figure S1
ID(sex)
1(M)
2(F)
3(M)
4(F)
5(F)
6(M)
7(F)
8(M)
9(M)
10(F)
1(M)
0.50
0.00
0.25
0.25
0.00
0.00
0.13
0.13
0.13
0.13
2(F)
0.00
0.50
0.25
0.25
0.00
0.00
0.13
0.13
0.13
0.13
3(M)
0.25
0.25
0.50
0.25
0.00
0.00
0.25
0.13
0.13
0.19
4(F)
0.25
0.25
0.25
0.50
0.00
0.00
0.13
0.25
0.25
0.19
5(F)
0.00
0.00
0.00
0.00
0.50
0.00
0.25
0.00
0.00
0.13
6(M)
0.00
0.00
0.00
0.00
0.00
0.50
0.00
0.25
0.25
0.13
7(F)
0.13
0.13
0.25
0.13
0.25
0.00
0.50
0.06
0.06
0.28
8(M)
0.13
0.13
0.13
0.25
0.00
0.25
0.06
0.50
0.50
0.28
9(M)
0.13
0.13
0.13
0.25
0.00
0.25
0.06
0.50
0.50
0.28
10(F)
0.13
0.13
0.19
0.19
0.13
0.13
0.28
0.28
0.28
0.53
Table S2 Kinship matrix on X chromosome for 10-member pedigree in Figure S1
ID(sex)
1(M)
2(F)
3(M)
4(F)
5(F)
6(M)
7(F)
8(M)
9(M)
10(F)
1(M)
1.00
0.00
0.00
0.50
0.00
0.00
0.00
0.50
0.50
0.25
2(F)
0.00
0.50
0.50
0.25
0.00
0.00
0.25
0.25
0.25
0.25
3(M)
0.00
0.50
1.00
0.25
0.00
0.00
0.50
0.25
0.25
0.38
4(F)
0.50
0.25
0.25
0.50
0.00
0.00
0.13
0.50
0.50
0.31
5(F)
0.00
0.00
0.00
0.00
0.50
0.00
0.25
0.00
0.00
0.13
6(M)
0.00
0.00
0.00
0.00
0.00
1.00
0.00
0.00
0.00
0.00
7(F)
0.00
0.25
0.50
0.13
0.25
0.00
0.50
0.13
0.13
0.31
8(M)
0.50
0.25
0.25
0.50
0.00
0.00
0.13
1.00
1.00
0.56
9(M)
0.50
0.25
0.25
0.50
0.00
0.00
0.13
1.00
1.00
0.56
10(F)
0.25
0.25
0.38
0.31
0.13
0.00
0.31
0.56
0.56
0.56
FIGURE LEGENDS:
Figure S1: A detailed pedigree plot with text added to the subject identifier. Subject symbols
show the status for three affected indicators, with a legend in the top right giving the portions
attributed to each variable.